ON THE OPTIMIZATION OF CONSERVATION LAW MODELS AT A JUNCTION WITH INFLOW AND FLOW DISTRIBUTION CONTROLS.

The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely, we consider a general class of junction distribution controls and inflow controls and we establish the compactness in L¹ of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges. [ABSTRACT FROM AUTHOR]